Boundary conditions applied on bearing corner in direct aluminum extrusion

Finite element analysis in aluminum extrusion is faced by several problems such as number of degrees of freedom, calculation time, large deformation and flow conservation. The problem of large deformation is overcome by applying the Eulerian formulation. But the problems concerning number of degrees of freedom, calculation time can be overcome by the model simplification especially at the bearing corner. On the one hand, detailed modeling of the bearing corner will increase the complexity of the analysis. On the other hand, simplified modeling of the bearing corner will face problems such as locking of the corner node and flow conservation. Therefore, boundary conditions will be applied at the corner node in order to solve the problem of its locking and to satisfy the aluminum flow conservation. These boundary conditions include normal and constraint equation. This paper focuses on the calculation of the normal with different elements such as plane strain, axisymmetric and tetrahedron elements. The constraint equation at different positions of the corner node is determined for a plane strain element only. The extrusion force and average exit velocity are investigated and compared with the triple node method and reference model. Where, in the reference model the contact boundary condition is applied between the rigid die and aluminum. Eulerian formulation is applied in finite element analysis unless in the reference model the Arbitrary Lagrangian Eulerian formulation is applied

3-D Numerical Simulation of Direct Aluminum Extrusion and Die Deformation

The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. Therefore, the die is designed by a trial and error method which is an expensive process. In addition, after several runs the die may deform. This may lead to an unacceptable product. This paper focuses on 3-D simulation of a direct aluminum extrusion process. The behavior of the billet and die is predicted. In the simulation an Eulerian formulation is applied to simulate the flow of the material, rather than an Updated Lagragian formulation with remeshing. Finally, the results will illustrate how the die deforms and whether it deforms elastically or plastically and the influence of die deformation on the extruded product dimensions

Single magnetic impurities in the Kane-Mele model

The realization of the spin-Hall effect in quantum wells has led to a plethora of studies regarding the properties of the edge states of a 2D topological insulator. These edge states constitute a class of one-dimensional liquids, called the helical liquid, where an electron's spin quantization axis is tied to its momentum. In contrast to one dimensional conductors, magnetic impurities - below the Kondo temperature - cannot block transport and one expects the current to circumvent the impurity. To study this phenomenon, we consider the single impurity Anderson model embedded into an edge of a Kane-Mele ribbon with up to 512x80 sites and use the numerically exact continuous time QMC method to study the Kondo effect. We present results on the temperature dependence of the spectral properties of the impurity and the bulk system that show the behaviour of the system in the various regimes of the Anderson model. A view complementary to the single particle spectral functions can be obtained using the spatial behaviour of the spin-spin correlation functions. Here we show the characteristic, algebraic decay in the edge channel near the impurity.Comment: 14 pages, 14 Figures, submitted to PR

Exact diagonalization study of the tunable edge magnetism in graphene

The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially we find that there are two important features of edge states: (a) umklapp processes are completely forbidden for edge states; this allows a spin-polarized ground state. (b) the strong momentum dependence of the effective interaction vertex for edge states gives rise to a regime of partial spin-polarization and a second order phase transition between a standard paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.Comment: 11 pages, 8 figure

Dynamic response of trapped ultracold bosons on optical lattices

We study the dynamic response of ultracold bosons trapped in one-dimensional optical lattices using Quantum Monte Carlo simulations of the boson Hubbard model with a confining potential. The dynamic structure factor reveals the inhomogeneous nature of the low temperature state, which contains coexisting Mott insulator and superfluid regions. We present new evidence for local quantum criticality and shed new light on the experimental excitation spectrum of 87Rb atoms confined in one dimension.Comment: 4 pages, 5 figure

Dynamic Exponent of t-J and t-J-W Model

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D \propto \delta^2$ for small doping concentration $\delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.Comment: LaTeX, JPSJ-style, 4 pages, 5 eps files, to appear in J. Phys. Soc. Jpn. vol.67, No.6 (1998

Effect of the W-term for a t-U-W Hubbard ladder

Antiferromagnetic and d_{x2-y2}-pairing correlations appear delicately balanced in the 2D Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy H_W was found to favor pairing. However, such a term can be separated into a number of simpler processes and one would like to know which of these terms are responsible for enhancing the pairing. Here we analyze these processes for a 2-leg Hubbard ladder

Quantum Transition between an Antiferromagnetic Mott Insulator and dx2−y2d_{x^2 - y^2} Superconductor in Two Dimensions

We consider a Hubbard model on a square lattice with an additional interaction, $W$, which depends upon the square of a near-neighbor hopping. At half-filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction $W$ drives the system from an antiferromagnetic Mott insulator to a $d_{x^2 -y^2}$ superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$.Comment: 4 pages (latex) and 4 postscript figure

Insulator-Metal Transition in the One and Two-Dimensional Hubbard Models

We use Quantum Monte Carlo methods to determine $T=0$ Green functions, $G(\vec{r}, \omega)$, on lattices up to $16 \times 16$ for the 2D Hubbard model at $U/t =4$. For chemical potentials, $\mu$, within the Hubbard gap, $|\mu | < \mu_c$, and at {\it long} distances, $\vec{r}$, $G(\vec{r}, \omega = \mu) \sim e^{ -|\vec{r}|/\xi_l}$ with critical behavior: $\xi_l \sim | \mu - \mu_c |^{-\nu}$, $\nu = 0.26 \pm 0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by $\nu = 1/2$ and $z = 2$.Comment: 9 pages (latex) and 5 postscript figures. Submitted for publication in Phys. Rev. Let